Locally forced critical surface waves in channels of arbitrary cross section
By utilizing the framework and assumption of \textit{J. W. Miles} [J. Fluid Mech. 162, 489-499 (1986; Zbl 0595.76017)] and invoking the assumption of localized forcing, the author derives analytic solutions of the forced Korteweg-de Vries equation. These results confirm the conclusions of the earlier numerical work of the author [Z. Angew. Math. Phys. 40, 216-229 (1989; Zbl 0668.76018)] and the author and \textit{M. C. Shen} [Eur. J. Mech. B 9, No.1, 59-74 (1990; Zbl 0692.76010)] about the structure of locally forced critical surface waves in channels of arbitrary cross- section. In particular, conditions are established under which the existence of two solitary wave solutions holds. This confirms the conjecture of Miles, and the observations of \textit{A. Patoine} and \textit{T. Warn} [J. Atmos. Sci. 39, 1018-1025 (1982)].
scientific article; zbMATH DE number 4206887
scientific article